Abstract

We are concerned with the nonlinear (𝑛+1)-term fractional integrodifferential inclusions 𝐿(𝐷)𝑢∈𝐹(𝑡,𝑢,𝑇𝑢,𝑆𝑢), 𝑎.𝑒.𝑡∈[0,1], where 𝐿(𝐷)=𝐷𝛼−𝑏𝑛𝐷𝛽𝑛−𝑏𝑛−1𝐷𝛽𝑛−1−⋯−𝑏1𝐷𝛽1, 0<𝛽1<𝛽2<⋯<𝛽𝑛−1<𝛽𝑛<1<𝛼<2, 𝑏1,𝑏2,…,𝑏𝑛 are constant coefficients, and ∫(𝑇𝑢)(𝑡)=10𝑘(𝑡,𝑠)𝑢(𝑠)𝑑𝑠, ∫(𝑆𝑢)(𝑡)=𝑡0𝑙(𝑡,𝑠)𝑢(𝑠)𝑑𝑠, subject to the nonlocal conditions 𝑢(0)=0, ∑𝑢(1)=𝑚𝑖=1𝛾𝑖𝑢(𝜂𝑖). The existence results are obtained by using two fixed-point theorems due to Bohnenblust-Karlin and Covitz-Nadler, respectively. Our results partly generalize and improve the known ones.